 Lsp =10 log

P 2
P ref ( )
=20 log
P
Pref
-
( ) −5
Pref =2.10 Pa : reference sound pressure

 Ln−sp=10 log
[ 1
n ( 10 +10 +…+ 100.1 L )
0.1 L 0.1 L 1 2 n
]
 Lsw =10 log
I
I ref ( ) -
−12 2
I ref =10 W /m : reference sound intensity – the threshold of hearing
Spherical distance – directivity coefficient Q=1 Sound pressure – Q
2 ρ.c. N N 2 Q.ρ.c .N
P= 2
I= 2
P= 2
4πr 4πr 4πr
SPL=SWL−20 log ( r )−11 SPL=SWL−20 log ( r )−11+10 log ( Q )

 dL=Lsp 2−Lsp 1=20 log

r2
r1 ()
 NB: at each frequency f , the SWL has correction factor db (A ) before make any calculation.
2
Absorption Quantification(coefficient): α =
Absorbed energy Sound Absorbed intensity (W / m )

n =
Incident energy Sound Incident intensity
 STL=10 log
( )
Wi
Wt
=10 log
1
at
(dB)

- W i : sound energy/power incident - W t : sound energy/power transmitted - a t : transmission coefficient

2
 A=S 1 α 1 +S 2 α 2 +…+ S n α n (m Sabine)
- Sn area of the surface n ( m2 ) - α n: absorption coefficient of surface n
A
 α m= ; S=S 1+ S 2+ …+S n: total surface in room (m 2)
S
V V
α m ≤0.35 → T a =0.16 α m >0.35 →T a=0.16

([ αA ) ln 1−α1 ]
A
m m

αm A
- N : sound power (W ) - Room absorption area (m 2 Sabine ): R s=S =
1−α m 1−α m
N 4N
 The total sound intensity: I= +
4πr
2
Rs
 Distance from source: r >1 m: received sound power level  Distance from source: r <1 m

SPL=SWL+10 log
Q
+
4 π r Rs
2
4
[ ] SPL=SWL−10 log V +10 log T a +13.9

Sound propagation in Free Filed: Sound propagation in Free Filed with directivity:
SPL=SWL−20 log ( r )−11 SPL=SWL−20 log ( r )−11+10 log ( Q )
Sound propagation in Reverberant room (r>1m): Sound propagation in Reverberant room (r<1m):

SPL=SWL+10 log
[ Q
+
4 π r Rs
2
4
] SPL=SWL−10 log V +10 log T a +13.9

Sound propagation room to room through partition: Sound propagation room to outside through partition:
S2 Q
SP L2=SP L1−SRI +10 log SP L2=SP L1−SRI +10 log S w +10 log 2
−6
A 4πr
S P L1: reverberant sound pressure in the room source1
SP L2: measuring sound pressure at position r from the partition
Single Plate Case
Region I: Stiffness-controlled region (low frequency: f <f 11 resonance frequency)


2
a t=K s ln 1+
( 1
K 2s )
- K s =4 πf . ρ .c . Cs
ρ : density of air C s: mechanical compliance per unit area

√
- for rectangular panel: - for circular panel:
E
c= : speed of sound within
768 ( 1−σ ) 2
3 D ( 1−σ )
4 2
ρm C s= C s=
( )
2 3
wall 8 1 1
3 256 E h
E: Young modulus of material π Eh 2+ 2
a b D diameter of panel
ρm : density of material
a and b width and height of panel
h : thickness of panel
σ : Poisson’s ratio of panel
 The transmission loss for Region I:

STL=20 log
( K1 )−10 log (0.23026 ST L )=20 log ( K1 )−10 log [ ln (1+ K1 )]
s
n
s
2
s

 The resonant frequency: (m=n=1) – rectangular plate  The resonant frequency: (m=n=1) – circular plate diameter D

( 4 √ 3 ) [( ) ( ) ]
π m
2
n
2 C Lh
f mn= CLh + f 11=10.2
π √3 D
2
a b

[ ]
1
E 2
C L= : speed of longitudinal sound waves within the wall
ρm ( 1−σ 2 )
Region II: Mass-controlled region ( f 11 < f < f c)

( ) ( )
2 2
1 πf . ρm h πf . M s
 The sound power transmission coefficient for normal incidence: =1+ =1+
atn ρ1 . c 1 ρ1 . c 1
- M s= ρm .h : surface mass or the panel mass per unit surface area
- ρ1 and c 1: density of sound in the air around the panel
- ρm : density of material - h : thickness of panel

 The transmission loss for Region II-normal incidence: ST Ln=10 log ( a1 )

tn
 The transmission loss for Region II- random field incidence: STL=ST Ln−5

[ ]
 The critical frequency: 1
E 2
√3 c2 C L= : speed of longitudinal sound waves
ρm ( 1−σ )
2
f c=
π CLh
Region III: Damping-controlled region ( f >f c)

[ ( )]
2
π Ms f c
 The transmission loss for Region III at critical frequency-normal incidence: ST Ln (f c )=10 log 1+
ρ1 . c 1

 The transmission loss for Region III- random field incidence: STL=ST Ln ( f c ) +10 log ( η ) +33.22 log
( ) f
fc
−5.7
- η: damping coefficient for panel material
Double Plate Case with air gap (d )
Regime A
( ρc
π( MS +MS )
1
<f < f 0
2
)
[( )]
1
c ρ 1 1 2
 The resonant frequency: f 0= +
2π d MS MS 1 2

- M S , M S : specific mass for panel 1 and 2

1 2

 The transmission loss for Regime A: STL=20 log ( M S + M S ) + 20 log ( f )−47.3

1 2

(
Regime B f 0 < f <
c
2 πd )
 The transmission loss for Regime B: STL=ST L1+ ST L2 +20 log ( 4 πfd
c )
Regime C f >( c
2 πd )
[ ]
4
STL=ST L1+ ST L2 +10 log
 The transmission loss for Regime C: 2
1+
α
- α surface absorption coefficient for panels
Tow layer plate
 The specific mass for the layered panel: M s= ρ1 h1 + ρ 2 h2
2 2
E1 h1−E 2 h 2
χ=
2 ( E1 h + E2 h )
1 2

Region II: Mass-controlled region ( f <f c)

[ ( )]
2
πf M s
STL=10 log 1+ −5
ρc

( )
1

c2 M s 2
The critical frequency: f c =
2π B
E 1 h31
[ ( )] E2 h32
[ ( )]
2 2
2χ 2χ
B= 1+3 1− + 1+3 1+
12 ( 1−σ 1 )
2
h1 12 ( 1−σ 2 )
2
h2
Region III: Damping-controlled region ( f >f c)

 The transmission loss: STL=ST Ln ( f c ) +10 log ( η ) +33.22 log ( ff )−5.7

c
- η: damping coefficient
2
( η1 E 1 h1 +η 2 E2 h2 ) ( h1 +h2 )
η=

[ ( )] [ ( )]
2 2
3 2χ 3 2χ
E 1 h1 1+3 1− + E2 h 2 1+3 1+
h1 h2